If the system of equations $$ \begin{aligned} & x+(\sqrt{2} \sin \alpha) y+(\sqrt{2} \cos \alpha) z=0 \\ & \mathrm{x}+(\cos \alpha) \mathrm{y}+(\sin \alpha) \mathrm{z}=0 \\ & \mathrm{x}+(\sin...
JEE MainMathematicsEasy
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QJEE MAIN 2024
If y=y(x) is the solution of the differential equation dydx+2y=sin(2x),y(0)=34, then y8 is equal to :
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QJEE MAIN 2024
One of the points of intersection of the curves $y=1+3 x-2 x^2$ and $y=\frac{1}{x}$ is $\left(\frac{1}{2}, 2\right)$. Let the area of the region enclosed by...
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The pressure and volume of an ideal gas are related as (Constant). The work done when the gas is taken from state to state is...
JEE MainPhysicsMedium
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QJEE MAIN
Two charged conducting spheres of radii a and b are connected to each other by a conducting wire. The ratio of charges of the two...
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QJEE MAIN 2024
Let the sum of the maximum and the minimum values of the function $f(x)=\frac{2 x^2-3 x+8}{2 x^2+3 x+8}$ be $\frac{m}{n}$, where $\operatorname{gcd}(\mathrm{m}, \mathrm{n})=1$. Then $\mathrm{m}+\mathrm{n}$...
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QJEE MAIN 2024
If the solution $y=y(x)$ of the differential equation $\left(x^4+2 x^3+3 x^2+2 x+2\right) d y-\left(2 x^2+2 x+3\right) d x=0$ satisfies $y(-1)=-\frac{\pi}{4}$, then $y(0)$ is equal to:
JEE MainMathematicsHard
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The output Y of following circuit for given inputs is :
JEE MainPhysicsMedium
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QJEE MAIN 2024
Let a rectangle ABCD of sides 2 and 4 be inscribed in another rectangle PQRS such that the vertices of the rectangle ABCD lie on...
JEE MainMathematicsHard
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QJEE MAIN 2024
The vertices of a triangle are A(-1,3),B(-2,2) and C(3,-1). A new triangle is formed by shifting the sides of the triangle by one unit inwards....
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QJEE MAIN
A LCR circuit is at resonance for a capacitor C, inductance L and resistance R. Now the value of resistance is halved keeping all other...
JEE MainPhysicsMedium
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QJEE MAIN 2024
A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in figure. If the...
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QJEE MAIN 2024
A solid sphere and a hollow cylinder roll up without slipping on same inclined plane with same initial speed v . The sphere and the...
JEE MainPhysicsMedium
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QJEE MAIN 2024
Three urns A, B and C contain 7 red, 5 black; 5 red, 7 black and 6 red, 6 black balls, respectively. One of the...
JEE MainMathematicsEasy
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QJEE MAIN 2024
Let d be the distance of the point of intersection of the lines x+63=y2=z+11 and x-74=y-93=z-42 from the point (7,8,9). Then d2+6 is equal to...
JEE MainMathematicsHard
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Two planets A and B having masses m1 and m2 move around the sun in circular orbits of $r_1$ and $\mathrm{r}_2$ radii respectively. If angular...
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QJEE MAIN 2024
A sphere of relative density σ and diameter D has concentric cavity of diameter d. The ratio of D/d, if it just floats on water...
JEE MainPhysicsHard
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QJEE MAIN 2024
Let $f: \mathrm{R} \rightarrow \mathrm{R}$ be a function given by $$ f(x)=\left\{\begin{array}{cl} \frac{1-\cos 2 x}{x^2} & , x<0 \\ \alpha & , x=0, \text {...
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QJEE MAIN 2024
A light emitting diode (LED) is fabricated using GaAs semiconducting material whose band gap is 1.42eV. The wavelength of light emitted from the LED is:
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QJEE MAIN 2024
Given below are two statements: Statement (I): When an object is placed at the centre of curvature of a concave lens, image is formed at...
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